Answer:
should be the number of teaspoons of vanilla used when 5 cups of flour is used in the recipe.
Step-by-step explanation:
We are given the following information in the question:
Number of teaspoons of vanilla used in a cookie recipe = ![\displaystyle\frac{1}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7B1%7D%7B2%7D)
Number of cups if flower used in a cookie recipe =
![\displaystyle\frac{3}{4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7B3%7D%7B4%7D)
In order to solve this problem we use the concept of ratios.
![\text{Ratio} = \displaystyle\frac{\text{Teaspoons of vanilla}}{\text{Cups of flour}}\\\\= \frac{\frac{1}{2}}{\frac{3}{4}} = \frac{4}{6} = \frac{2}{3} = 2:3](https://tex.z-dn.net/?f=%5Ctext%7BRatio%7D%20%3D%20%5Cdisplaystyle%5Cfrac%7B%5Ctext%7BTeaspoons%20of%20vanilla%7D%7D%7B%5Ctext%7BCups%20of%20flour%7D%7D%5C%5C%5C%5C%3D%20%5Cfrac%7B%5Cfrac%7B1%7D%7B2%7D%7D%7B%5Cfrac%7B3%7D%7B4%7D%7D%20%3D%20%5Cfrac%7B4%7D%7B6%7D%20%3D%20%5Cfrac%7B2%7D%7B3%7D%20%3D%202%3A3)
This ratio could be interpreted as 2 teaspoons of vanilla would require 3 cups of flower in the cookie recipe.
Now, we want how much vanilla to use when we have 5 cups of flower. Let x be the amount of vanilla required, then, we have:
![\displaystyle\frac{2}{3} = \frac{x}{5}\\\\x = \frac{10}{3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7B2%7D%7B3%7D%20%3D%20%5Cfrac%7Bx%7D%7B5%7D%5C%5C%5C%5Cx%20%3D%20%5Cfrac%7B10%7D%7B3%7D)
Hence,
should be the number of teaspoons of vanilla used when 5 cups of flour is used in the recipe.